Newsportal USENET - Re: True on the basis of meaning --- Good job Richard ! ---Socratic method MTT

Re: True on the basis of meaning --- Good job Richard ! ---Socratic method MTT

Sujet : Re: True on the basis of meaning --- Good job Richard ! ---Socratic method MTT
De : richard (at) *nospam* damon-family.org (Richard Damon)
Groupes : sci.logic comp.theory
Date : 29. May 2024, 04:38:41

Autres entêtes

Organisation : i2pn2 (i2pn.org)
Message-ID : <v36801$2d368$2@i2pn2.org>
References : 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
User-Agent : Mozilla Thunderbird

On 5/28/24 10:39 PM, olcott wrote:

On 5/28/2024 9:04 PM, Richard Damon wrote:
On 5/28/24 10:59 AM, olcott wrote:
On 5/28/2024 1:59 AM, Mikko wrote:
On 2024-05-27 14:34:14 +0000, olcott said:
>
?- LP = not(true(LP)).
LP = not(true(LP)).
>
?- unify_with_occurs_check(LP, not(true(LP))).
false.
>
In other words Prolog has detected a cycle in the directed graph of the
evaluation sequence of the structure of the Liar Paradox. Experts seem
to think that Prolog is taking "not" and "true" as meaningless and is
only evaluating the structure of the expression.
>
The words "not" and "true" of Prolog are meaningful in some contexts
but not above. The word "true" is meaningful only when it has no arguments.
>
>
That Prolog construes any expression having the same structure as the
Liar Paradox as having a cycle in the directed graph of its evaluation
sequence already completely proves my point. In other words Prolog
is saying that there is something wrong with the expression and it must
be rejected.
>
But Prolog doesn't support powerful enough logic to handle the system like Tarski and Godel are talking about.
>
The fact that Prolog just rejects it shows that.
>
Your ignorance is no excuse.

What ignorance?
The fact that I understand the limitation of Prolog and what forms of logic it can do, which seems to be beyond your understanding?
Claiming that Prolog rejects a statement because it doesn't fit its grammer is meaningless for more complicated logics that don't have that same grammer restricition.
IF you want to limit the logic you use to what Prolog can handle, go ahead, the rest of the world likes its mathematics.

>
You could try
?- LP = not(true(LP), true(LP).
>
or
?- LP = not(true(LP), not(true(LP)).
>
The predicate unify_with_occurs_check checks whether the resulting
sructure is acyclic because that is its purpose. Whether a simple
>
Yes exactly. If I knew that Prolog did this then I would not have
created Minimal Type Theory that does this same thing. That I did
create MTT that does do this same thing makes my understanding much
deeper.
>
unification like LP = not(true(LP)) does same is implementation
dependent as Prolog rules permit but do not require that. In a
typical implementation a simple unification does not check for
cycles.
>
>
ISO Prolog implementations have the built-in predicate
unify_with_occurs_check/2 for sound unification
https://en.wikipedia.org/wiki/Occurs_check#Sound_unification
>
Alternatively such expressions crash or remain stuck in infinite loops.
>
>
Anyway, none of this is relevant to the topic of this thread or
topics of sci.logic.
>
>
    ...14 Every epistemological antinomy can likewise be used for
    a similar undecidability proof...(Gödel 1931:40)
>
Gödel, Kurt 1931.
On Formally Undecidable Propositions of Principia Mathematica And Related Systems
>
https://monoskop.org/images/9/93/Kurt_G%C3%B6del_On_Formally_Undecidable_Propositions_of_Principia_Mathematica_and_Related_Systems_1992.pdf
>
    It would
    then be possible to reconstruct the *antinomy of the liar* in the
    metalanguage, by forming in the language itself a sentence x
    such that the sentence of the metalanguage which is correlated
    with x asserts that x is not a true sentence.
>
CONCEPT OF TRUTH IN FORMALIZED LANGUAGES, Tarski
https://liarparadox.org/Tarski_247_248.pdf
>
The Liar Paradox and other such {epistemological antinomies} must be
rejected as type mismatch errors for any system of bivalent logic thus
cannot be correctly used for any undecidability or undefinability proof.
>
>
But you just don't don't understand what was done in those proofs.
>
Neither of them assumed the Liar's paradox had a truth value. Only statements formed from VALID logical sequences in the field.
>
Please try to show what step in Godel's or Tarski's proof where they made a logical error (not just came up with a statement you think can't be valid).
>
Tarski's Liar Paradox from page 248
    It would then be possible to reconstruct the antinomy of the liar
    in the metalanguage, by forming in the language itself a sentence
    x such that the sentence of the metalanguage which is correlated
    with x asserts that x is not a true sentence.
    https://liarparadox.org/Tarski_247_248.pdf

Right, He has SHOWN that the logic system, when given the assumption of the existance of the Truth Predicate, can construct the liar as a truth-bearing statement.
That means the logic system must be inconsistant.
The ONLY added assumption to the system, that was initially required to be conssistant, was the existance of the Truth Predicate, so that assumption must be incorrect.
If you try your idea that the statement somehow gets intercepted as a type error, then all you have done is shown that you can, by your detecting the type error, is prove the new system with the truth predicate is inconsistant, so we STILL get to the assumption of a truth predicate can't be correct, and your traps must reject THAT statement as the source of the problem.

Formalized as:
x ∉ True if and only if p
where the symbol 'p' represents the whole sentence x
https://liarparadox.org/Tarski_275_276.pdf
adapted to become the first line of his proof
x ∉ Pr if and only if p

But that isn't the first line of the full proof, but a consequence from his previous logic.
A system that can prove a non-truth-bearer (or a 'syntax error') is an inconsistent system.

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Date	Sujet	#	Auteur
14 May 24	Re: True on the basis of meaning --- Good job Richard !	113	Richard Damon
14 May 24	Re: True on the basis of meaning --- Good job Richard !	2	olcott
14 May 24	Re: True on the basis of meaning --- Good job Richard !	1	Richard Damon
14 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	110	olcott
14 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	109	Richard Damon
14 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	2	olcott
14 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	1	Richard Damon
14 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	5	olcott
14 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	4	Richard Damon
14 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	1	wij
14 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	2	olcott
15 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	1	Richard Damon
15 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	2	olcott
15 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	1	Richard Damon
15 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	4	olcott
15 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	3	Richard Damon
15 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	2	olcott
16 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	1	Richard Damon
16 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	4	olcott
16 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	1	Richard Damon
16 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	2	immibis
16 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	1	olcott
16 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	2	olcott
16 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	1	Richard Damon
16 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	89	olcott
16 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	88	Richard Damon
16 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	87	olcott
16 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	86	Richard Damon
16 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	2	olcott
16 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	1	Richard Damon
16 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	5	olcott
16 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	4	Richard Damon
16 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	3	olcott
17 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	2	Richard Damon
17 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	1	olcott
16 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	78	olcott
16 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	77	Richard Damon
16 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	76	olcott
17 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	75	Richard Damon
17 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	74	olcott
17 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	73	Richard Damon
17 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	72	olcott
17 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	71	Richard Damon
17 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	68	olcott
17 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	67	Richard Damon
17 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	66	olcott
18 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	65	Richard Damon
18 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	64	olcott
18 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	63	Richard Damon
18 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	62	olcott
18 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	61	Richard Damon
18 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	60	olcott
18 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	59	Richard Damon
18 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	58	olcott
18 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	57	Richard Damon
18 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	56	olcott
18 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	55	Richard Damon
18 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	54	olcott
18 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	53	Richard Damon
18 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	2	olcott
18 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	1	Richard Damon
18 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	50	olcott
18 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	49	Richard Damon
18 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	48	olcott
19 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	47	Richard Damon
19 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	46	olcott
19 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	45	Richard Damon
19 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	44	olcott
19 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	43	Richard Damon
19 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	42	olcott
19 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	15	Richard Damon
19 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	14	olcott
20 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	12	Richard Damon
20 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	11	olcott
21 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	10	Richard Damon
21 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	9	olcott
21 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	8	Richard Damon
21 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	7	olcott
21 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	6	Richard Damon
21 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	5	olcott
21 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	4	Richard Damon
21 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	3	olcott
21 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	1	immibis
22 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	1	Richard Damon
20 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	1	immibis
20 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	26	olcott
22 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method (agreement)	25	olcott
23 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method (agreement)	24	Richard Damon
23 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method (agreement)	23	olcott
23 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method (agreement)	21	Richard Damon
23 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method (agreement)	6	olcott
23 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method (agreement)	5	Richard Damon
23 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method (agreement)	4	olcott
23 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method (agreement)	3	Richard Damon
23 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method (agreement)	2	olcott
24 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method (agreement)	1	Richard Damon
25 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method (agreement)	14	olcott
27 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method (agreement)	13	olcott
27 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method MTT	12	olcott
28 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method MTT	11	olcott
29 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method MTT	10	Richard Damon
23 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method (agreement)	1	olcott
17 May 24	Re: True on the basis of meaning --- Good job Richard ! ---Socratic method	2	olcott